# -*- Mode: shell-script -*-
#############################################################################
##
#A  trans8.grp                  GAP group library            Alexander Hulpke
#A                                                              & Greg Butler
#A                                                               & John McKay
##
##
#Y  Copyright (C) 2018-2021, Carnegie Mellon University
#Y  All rights reserved.  See LICENSE for details.
#Y  
#Y  This work is based on GAP version 3, with some files from version 4.  GAP is
#Y  Copyright (C) (1987--2021) by the GAP Group (www.gap-system.org).
##
##  This file contains the transitive groups of degree 8.
##
##


TRANSGRP[8]:=[
[(1,2,3,4,5,6,7,8),"C(8) = 8"],
[(1,2,3,8)(4,5,6,7),(1,5)(2,6)(3,7)(4,8),"4[x]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),"E(8) = 2[x]2[x]2"],
[(1,2,3,8)(4,5,6,7),(1,6)(2,5)(3,4)(7,8),"D_8(8) = [4]2"]
,[(1,2,3,8)(4,5,6,7),(1,7,3,5)(2,6,8,4),"Q_8(8)"],
[(1,2,3,4,5,6,7,8),(1,6)(2,5)(3,4)(7,8),"D(8)"],
[(1,2,3,4,5,6,7,8),(1,5)(3,7),"1/2[2^3]4"],
[(1,2,3,4,5,6,7,8),(1,3)(2,6)(5,7),"2D_8(8) = [D(4)]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(4,5)(6,7),"E(8):2 = D(4)[x]2"],
[(1,5)(3,7),(1,2,3,8)(4,5,6,7),"[2^2]4"],
[(1,5)(3,7),(1,3,5,7)(2,4,6,8),(1,4,5,8)(2,3,6,7),"1/2[2^3]E(4) = Q_8:2"],
[(1,3,5,7)(2,4,6,8),(1,3,8)(4,5,7),"2A_4(8) = [2]A(4) = SL(2,3)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,3)(4,6,5),"E(8):3 = A(4)[x]2"],
[(1,3)(2,8)(4,6)(5,7),(1,2,3)(5,6,7),
(1,4)(2,6)(3,7)(5,8),"S(4)[1/2]2 = 1/2(S_4[x]2)"],
[(1,2,3,4,5,6,7,8),(1,5)(3,7),(1,6)(2,5)(3,4)(7,8),"[1/4.cD(4)^2]2"],
[(2,6)(3,7),(1,2,3,4,5,6,7,8),"1/2[2^4]4"],
[(1,2,3,8),(1,5)(2,6)(3,7)(4,8),"[4^2]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(4,5)(6,7),(4,6)(5,7),"E(8):E_4 = [2^2]D(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,3)(4,5,6,7),"E(8):4 = [1/4.eD(4)^2]2"]
,[(2,6)(3,7),(1,2,3,8)(4,5,6,7),"[2^3]4"],
[(1,5)(3,7),(1,4,5,8)(2,3)(6,7),(1,3)(2,8)(4,6)(5,7),
"1/2[2^4]E(4) = [1/4.dD(4)^2]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(2,3)(4,5),(2,3)(6,7),"E(8):D_4 = [2^3]2^2"],
[(1,2,3,4,5,6,7,8),(1,3,8)(4,5,7),"2S_4(8) = GL(2,3)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,3)(4,6,5),(2,3)(4,5),"E(8):D_6 = S(4)[x]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,6,3,4,5,7),"E(8):7 = F_56(8)"],
[(1,2,3,4,5,6,7,8),(1,5)(4,8),(1,7)(3,5)(4,8),
"1/2[2^4]eD(4)"],[(4,8),(1,2,3,8)(4,5,6,7),"[2^4]4"],
[(2,6)(3,7),(1,3)(5,7),(1,2,3,4,5,6,7,8),"1/2[2^4]dD(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,3)(4,5,6,7),(1,3)(5,7),"E(8):D_8 = [2^3]D(4)"],
[(2,6)(3,7),(1,3)(4,8)(5,7),(1,2,3,8)(4,5,6,7),"1/2[2^4]cD(4)"],
[(4,8),(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),"[2^4]E(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,3)(4,6,5),(2,5)(3,4),"[2^3]A(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),(1,5)(2,6)(3,7)(4,8),
(1,2,3)(4,6,5),(4,6)(5,7),"E(8):A_4 = [1/3.A(4)^2]2 = E(4):6"],
[(1,8)(2,3),(1,2,3)(5,6,7),(1,5)(2,7)(3,6)(4,8),
"1/2[E(4)^2:S_3]2 = E(4)^2:D_6"],
[(4,8),(1,3)(5,7),(1,2,3,8)(4,5,6,7),"[2^4]D(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,6,3,4,5,7),(1,2,3)(4,6,5),"E(8):F_21"],
[(1,2,3,4,5,6,8),(1,2,4)(3,6,5),(1,6)(2,3)(4,5)(7,8),"L(8) = PSL(2,7)"],
[(4,8),(1,8)(2,3)(4,5)(6,7),(1,2,3)(5,6,7),"[2^4]A(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),
(1,5)(2,6)(3,7)(4,8),(1,2,3)(4,6,5),(1,6)(2,3,5,4),"[2^3]S(4)"],
[(1,5)(4,8),(1,8)(2,3)(4,5)(6,7),(1,2,3)(5,6,7),
(2,3)(4,8)(6,7),"1/2[2^4]S(4)"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),(1,5)(2,6)(3,7)(4,8),
(1,2,3)(4,6,5),(1,3)(4,5,6,7),"E(8):S_4 = [E(4)^2:S_3]2 = E(4)^2:D_12"],
[(1,3)(2,8),(1,2,3),(1,5)(2,6)(3,7)(4,8),"[A(4)^2]2"],
[(1,2,3,4,5,6,8),(1,3,2,6,4,5),(1,6)(2,3)(4,5)(7,8),"L(8):2 = PGL(2,7)"],
[(4,8),(1,8)(4,5),(1,2,3,8)(4,5,6,7),"[2^4]S(4)"],
[(1,3)(2,8),(1,2,3),(1,8)(4,5),(1,5)(2,6)(3,7)(4,8),"[1/2.S(4)^2]2"],
[(1,3)(2,8),(1,2,3),(1,8)(4,5),(1,5)(2,7,3,6)(4,8),"1/2[S(4)^2]2"],
[(1,2,3,8),(2,3),(1,5)(2,6)(3,7)(4,8),"[S(4)^2]2"],
[(1,8)(2,3)(4,5)(6,7),(1,3)(2,8)(4,6)(5,7),(1,5)(2,6)(3,7)(4,8),
(1,2,6,3,4,5,7),(1,2,3)(4,6,5),(1,2)(5,6),"E(8):L_7 = AL(8)"],
[(1,7,8),(2,7,8),(3,7,8),(4,7,8),(5,7,8),(6,7,8),"A(8)"],
[(1,8),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),"S(8)"]];

TRANSPROPERTIES[8]:=
[[8,0,1,-1,[F,F,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-2008,-4],[-6008],[-6008]],
[8,0,1,1,[F,F,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-1004,4,1008],[6008],[6008]],
[8,0,1,1,[F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F],
[6004],[6008],[6008]],
[8,0,1,1,[F,F,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-3004,4,8],[6008],[6008]],
[8,0,1,1,[F,F,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[4,2008],[6008],[6008]],
[16,0,1,-1,[F,F,T,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-2008,-4],[-8,2016],[-2008,1016]],
[16,0,1,-1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-2008,1016],[-2008,1016]],
[16,0,1,-1,[F,F,T,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,2016],[-2008,1016]],
[16,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-1004,4,1008],[1016,2008],[1016,2008]],
[16,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-2004,16],[1016,2008],[1016,2008]],
[16,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[4,2008],[1016,2008],[1016,2008]],
[24,0,1,1,[F,F,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,T,F,F],
[4,24],[8,1024],[8,1024]],
[24,0,1,1,[F,F,F,T,F,F,F,T,F,F,F,F,F,F,F,F,F,F,T,F,F],
[4,1012],[8,1024],[8,1024]],
[24,0,1,1,[F,F,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-12,-4,12],[8,1024],[8,1024],[4,[-1012,-6,-2,6,8,24]]],
[32,0,1,-1,[F,T,T,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,16,32],[-8,2016]],
[32,0,1,-1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,2016],[-2008,32],[29,[-1004],[1008],[1008],[1008]]],
[32,0,1,-1,[F,T,F,T,F,F,F,F,F,T,F,T,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-2008,32],[-8,16,32]],
[32,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-2004,16],[32,2008],[8,2016]],
[32,0,1,1,[F,T,F,T,F,F,F,F,F,F,T,F,F,T,F,F,F,F,F,F,F],
[-8,-4,16],[8,16,32],[8,16,32],[604,[1,3]]],
[32,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[-8,-4,16],[8,2016],[32,2008]],
[32,0,1,-1,[F,T,F,T,F,F,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F],
[4,2008],[-8,2016],[-2008,32],[29,[-1004],[1008],[1008],[1008]]],
[32,0,1,1,[F,T,F,T,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F],
[4,2008],[8,2016],[32,2008]],
[48,0,1,-1,[F,F,T,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,T,F,T],
[-24,-4],[-8,48],[-1024,-8]] ,
[48,0,1,1,[F,T,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,T,F,F],
[-12,-4,12],[8,1024],[8,1024],[4,[-6,-2,6,8,1024]]],
[56,1,2,1,[F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F],
[28],[56],[56],[607,[1]],[4,[14,56]]],
[64,0,1,-1,[F,T,T,T,F,F,F,F,F,T,F,T,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,16,32],[-8,16,32],[22,[4],[8],[1008]],[29,[8],[16],[1016]]],
[64,0,1,-1,[T,T,T,T,F,F,F,F,F,F,F,T,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,2016],[-2008,32],
[29,[8],[16],[16],[16]]],
[64,0,1,-1,[F,T,F,T,F,F,F,F,F,F,T,T,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,16,32],[-8,16,32],[29,[-1004],[1008],[1016]]],
[64,0,1,1,[F,T,F,T,F,F,F,F,F,F,T,F,F,T,F,F,F,F,F,F,F],
[-8,-4,16],[8,16,32],[8,16,32],[604,[3,3]]],
[64,0,1,-1,[F,T,T,T,F,F,F,F,F,T,F,T,F,T,F,F,F,F,F,F,F],
[-8,-4,16],[-8,16,32],[-8,16,32],[22,[-4],[-8],[16]],
[29,[8],[16],[1016]]],
[64,0,1,-1,[T,T,T,T,F,F,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F],
[4,2008],[-8,2016],[-2008,32],[29,[8],[16],[16],[16]]],
[96,0,1,1,[F,T,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,T,F,F],
[4,24],[8,48],[24,32]],
[96,0,1,1,[F,T,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,T,F,F],
[12,16],[24,32],[8,48],[4,[-12,-2,24,32]],[606,[4]]],
[96,0,1,1,[F,T,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F],
[12,16],[24,32],[8,48],[4,[-2012,-2,32]]],
[128,0,1,-1,[T,T,T,T,F,F,F,F,F,T,T,T,F,T,F,F,F,F,F,F,T],
[-8,-4,16],[-8,16,32],[-8,16,32],[29,[8],[16],[32]]],
[168,1,2,1,[F,F,F,T,F,F,F,T,F,F,F,F,F,F,F,F,F,F,T,T,F],
[28],[56],[56],[607,[3]],[4,[14,56]]],
[168,1,2,1,[F,F,F,T,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,T,F],
[28],[56],[56],[4,[42,1014]]],
[192,0,1,-1,[T,T,T,T,F,F,F,T,T,F,F,T,F,T,F,F,F,T,T,F,F],
[4,24],[-8,48],[-24,32]],
[192,0,1,1,[F,T,F,T,F,F,F,T,F,F,T,F,F,T,F,F,F,F,T,F,F],
[-24,-4],[8,48],[24,32]],
[192,0,1,-1,[F,T,T,T,F,F,F,T,F,T,F,T,F,T,F,F,F,F,T,F,T],
[-24,-4],[-8,48],[-24,32],[22,[4],[24]]],
[192,0,1,1,[F,T,F,T,F,F,F,T,F,F,T,F,F,T,F,F,F,F,T,F,F],
[12,16],[24,32],[8,48],[4,[-12,-2,24,32]],[606,[7]]],
[288,0,1,1,[F,T,F,T,T,F,T,T,F,F,F,F,F,T,F,F,F,F,T,F,F],
[12,16],[24,32],[8,48],[4,[-36,-2,32]],[2129,[12,72,1024]]],
[336,1,3,-1,[F,F,T,T,F,F,F,T,F,F,F,F,F,T,F,F,F,T,F,T,T],
[28],[-56],[-56],[4,[28,42]]],
[384,0,1,-1,[T,T,T,T,F,F,F,T,T,T,T,T,F,T,F,F,F,T,T,F,T],
[-24,-4],[-8,48],[-24,32],[22,[-4],[-24]]],
[576,0,1,1,[F,T,F,T,T,F,T,T,F,F,T,F,F,T,F,F,F,F,T,F,F],
[12,16],[24,32],[8,48],[4,[-36,-2,32]],[2129,[12,48,72]]],
[576,0,1,-1,[F,T,F,T,T,F,T,T,F,F,T,T,F,T,F,F,F,F,F,F,T],
[12,16],[-24,32],[-8,48],[29,[-1012],[1016]]],
[1152,0,1,-1,[T,T,T,T,T,T,T,T,F,T,T,T,T,T,F,F,F,F,T,F,T],
[12,16],[-24,32],[-8,48],[29,[24],[32]]],
[1344,1,3,1,[F,T,F,T,F,F,F,T,F,F,T,F,F,T,F,F,F,F,T,T,F],
[28],[56],[56],[4,[14,56]],[607,[5]]],
[20160,1,6,1,[F,T,F,T,T,F,T,T,F,F,T,F,F,T,T,F,T,F,T,T,F],
[28],[56],[56],[4,[70]]],
[40320,1,8,-1,[T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T],
[28],[-56],[-56],[4,[70]]]];

